Chord transformations occur when a chord voicing is altered and transforms that chord into a different one. For example, if you have a C major chord and the move the tonic half-step down, you will get the inverted Em chord with the notes B, E and G:
Triads and seventh chords can easily be altered with parsimonious voice-leading so that they become different chords, often with a different function. If that is the case, you can modulate from one key to another by altering a given chord in the original key so that it points towards a cadence in a new key.
One of such examples is when you alter any chord voice of a diminished 7th chord by half-step down you will get dominant chords separated by minor thirds. As seen, if you consider a Bᵒ7 chord with the notes B, D, F and Ab and move the tonic, you will get a Bb7 chord. Applying the same procedure to the rest of the chord voices you will end up with a C#7 or Db7 , E7 and G7 chords and being dominant chords, they can all point to different tonics.
The motion between approximate harmonies can be described by simple chord voicings transformations, regardless of how the voices are distributed in register. The three main transformations, according to the Neo-Riemannian triadic theory, move one of the notes of a given triad to produce a different triad:
- The Parallel (P) – converts a major chord into a minor chord by moving the third of the chord a half-step down, or the reverse to convert a minor chord into major by moving the third a half-step up – C to Cm and vice-versa:
- The Relative (R) – converts a major triad to its relative minor triad by moving the fifth of the chord a whole-step up, and a minor chord into its relative major by moving the tonic a whole-step down – C to Am and vice-versa:
- The Leading-tone (L) – converts a major triad to a minor triad by moving the root or the tonic of the chord a half-step down, or by moving the fifth of a minor chord a half-step up – C to Em and vice-versa:
- The Slide Transformation (S) – by preserving the third of both chords, it moves the tonic and dominant by a parallel up, in major chords, or down a half-step, in case of minor chords:
By combining more than one of the presented operations above, it is possible to get chords other than the parallel, mediant or submediant – i.e. C major can be transformed in Cm, Em or Am. This means that you can apply successive transformations and use the resulting chord progression.
An example of a successive transformation starting in C, using L + R + P + L + S, will turn out the following chord succession:
The importance of the Neo-Riemannian theory lies in the ability to describe and relate these non-functional chord successions that were in use in the mid nineteenth century. Despite the fact that the music produced using this kind of chromatic chord progression approach can be pleasing, it is still non-functional according to tonal harmony.
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